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AbstractMultipleLinearRegression (Commons Math 3.2 API)
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org.apache.commons.math3.stat.regression</FONT>
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Class AbstractMultipleLinearRegression</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.stat.regression.AbstractMultipleLinearRegression</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</A></DD>
</DL>
<DL>
<DT><B>Direct Known Subclasses:</B> <DD><A HREF="../../../../../../org/apache/commons/math3/stat/regression/GLSMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">GLSMultipleLinearRegression</A>, <A HREF="../../../../../../org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html" title="class in org.apache.commons.math3.stat.regression">OLSMultipleLinearRegression</A></DD>
</DL>
<HR>
<DL>
<DT><PRE>public abstract class <B>AbstractMultipleLinearRegression</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</A></DL>
</PRE>

<P>
Abstract base class for implementations of MultipleLinearRegression.
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>2.0</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: AbstractMultipleLinearRegression.java 1416643 2012-12-03 19:37:14Z tn $</DD>
</DL>
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<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#AbstractMultipleLinearRegression()">AbstractMultipleLinearRegression</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected abstract &nbsp;<A HREF="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateBeta()">calculateBeta</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the beta of multiple linear regression in matrix notation.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected abstract &nbsp;<A HREF="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateBetaVariance()">calculateBetaVariance</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the beta variance of multiple linear regression in matrix
 notation.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateErrorVariance()">calculateErrorVariance</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the variance of the error term.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateResiduals()">calculateResiduals</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the residuals of multiple linear regression in matrix
 notation.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#calculateYVariance()">calculateYVariance</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the variance of the y values.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateErrorVariance()">estimateErrorVariance</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Estimates the variance of the error.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressandVariance()">estimateRegressandVariance</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the variance of the regressand, ie Var(y).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParameters()">estimateRegressionParameters</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Estimates the regression parameters b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParametersStandardErrors()">estimateRegressionParametersStandardErrors</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the standard errors of the regression parameters.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[][]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionParametersVariance()">estimateRegressionParametersVariance</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Estimates the variance of the regression parameters, ie Var(b).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateRegressionStandardError()">estimateRegressionStandardError</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Estimates the standard error of the regression.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#estimateResiduals()">estimateResiduals</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Estimates the residuals, ie u = y - X*b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#getX()">getX</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#getY()">getY</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#isNoIntercept()">isNoIntercept</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newSampleData(double[], int, int)">newSampleData</A></B>(double[]&nbsp;data,
              int&nbsp;nobs,
              int&nbsp;nvars)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Loads model x and y sample data from a flat input array, overriding any previous sample.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newXSampleData(double[][])">newXSampleData</A></B>(double[][]&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Loads new x sample data, overriding any previous data.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newYSampleData(double[])">newYSampleData</A></B>(double[]&nbsp;y)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Loads new y sample data, overriding any previous data.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#setNoIntercept(boolean)">setNoIntercept</A></B>(boolean&nbsp;noIntercept)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#validateCovarianceData(double[][], double[][])">validateCovarianceData</A></B>(double[][]&nbsp;x,
                       double[][]&nbsp;covariance)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Validates that the x data and covariance matrix have the same
 number of rows and that the covariance matrix is square.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#validateSampleData(double[][], double[])">validateSampleData</A></B>(double[][]&nbsp;x,
                   double[]&nbsp;y)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Validates sample data.</TD>
</TR>
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<A NAME="AbstractMultipleLinearRegression()"><!-- --></A><H3>
AbstractMultipleLinearRegression</H3>
<PRE>
public <B>AbstractMultipleLinearRegression</B>()</PRE>
<DL>
</DL>

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<A NAME="getX()"><!-- --></A><H3>
getX</H3>
<PRE>
protected <A HREF="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>getX</B>()</PRE>
<DL>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the X sample data.</DL>
</DD>
</DL>
<HR>

<A NAME="getY()"><!-- --></A><H3>
getY</H3>
<PRE>
protected <A HREF="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>getY</B>()</PRE>
<DL>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the Y sample data.</DL>
</DD>
</DL>
<HR>

<A NAME="isNoIntercept()"><!-- --></A><H3>
isNoIntercept</H3>
<PRE>
public boolean <B>isNoIntercept</B>()</PRE>
<DL>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>true if the model has no intercept term; false otherwise<DT><B>Since:</B></DT>
  <DD>2.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="setNoIntercept(boolean)"><!-- --></A><H3>
setNoIntercept</H3>
<PRE>
public void <B>setNoIntercept</B>(boolean&nbsp;noIntercept)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>noIntercept</CODE> - true means the model is to be estimated without an intercept term<DT><B>Since:</B></DT>
  <DD>2.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="newSampleData(double[], int, int)"><!-- --></A><H3>
newSampleData</H3>
<PRE>
public void <B>newSampleData</B>(double[]&nbsp;data,
                          int&nbsp;nobs,
                          int&nbsp;nvars)</PRE>
<DL>
<DD><p>Loads model x and y sample data from a flat input array, overriding any previous sample.
 </p>
 <p>Assumes that rows are concatenated with y values first in each row.  For example, an input
 <code>data</code> array containing the sequence of values (1, 2, 3, 4, 5, 6, 7, 8, 9) with
 <code>nobs = 3</code> and <code>nvars = 2</code> creates a regression dataset with two
 independent variables, as below:
 <pre>
   y   x[0]  x[1]
   --------------
   1     2     3
   4     5     6
   7     8     9
 </pre>
 </p>
 <p>Note that there is no need to add an initial unitary column (column of 1's) when
 specifying a model including an intercept term.  If <A HREF="../../../../../../org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#isNoIntercept()"><CODE>isNoIntercept()</CODE></A> is <code>true</code>,
 the X matrix will be created without an initial column of "1"s; otherwise this column will
 be added.
 </p>
 <p>Throws IllegalArgumentException if any of the following preconditions fail:
 <ul><li><code>data</code> cannot be null</li>
 <li><code>data.length = nobs * (nvars + 1)</li>
 <li><code>nobs > nvars</code></li></ul>
 </p>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>data</CODE> - input data array<DD><CODE>nobs</CODE> - number of observations (rows)<DD><CODE>nvars</CODE> - number of independent variables (columns, not counting y)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if the data array is null
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the length of the data array is not equal
 to <code>nobs * (nvars + 1)</code>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A></CODE> - if <code>nobs</code> is smaller than
 <code>nvars</code></DL>
</DD>
</DL>
<HR>

<A NAME="newYSampleData(double[])"><!-- --></A><H3>
newYSampleData</H3>
<PRE>
protected void <B>newYSampleData</B>(double[]&nbsp;y)</PRE>
<DL>
<DD>Loads new y sample data, overriding any previous data.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>y</CODE> - the array representing the y sample
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if y is null
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if y is empty</DL>
</DD>
</DL>
<HR>

<A NAME="newXSampleData(double[][])"><!-- --></A><H3>
newXSampleData</H3>
<PRE>
protected void <B>newXSampleData</B>(double[][]&nbsp;x)</PRE>
<DL>
<DD><p>Loads new x sample data, overriding any previous data.
 </p>
 The input <code>x</code> array should have one row for each sample
 observation, with columns corresponding to independent variables.
 For example, if <pre>
 <code> x = new double[][] {{1, 2}, {3, 4}, {5, 6}} </code></pre>
 then <code>setXSampleData(x) </code> results in a model with two independent
 variables and 3 observations:
 <pre>
   x[0]  x[1]
   ----------
     1    2
     3    4
     5    6
 </pre>
 </p>
 <p>Note that there is no need to add an initial unitary column (column of 1's) when
 specifying a model including an intercept term.
 </p>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the rectangular array representing the x sample
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if x is null
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if x is empty
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if x is not rectangular</DL>
</DD>
</DL>
<HR>

<A NAME="validateSampleData(double[][], double[])"><!-- --></A><H3>
validateSampleData</H3>
<PRE>
protected void <B>validateSampleData</B>(double[][]&nbsp;x,
                                  double[]&nbsp;y)
                           throws <A HREF="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</A></PRE>
<DL>
<DD>Validates sample data.  Checks that
 <ul><li>Neither x nor y is null or empty;</li>
 <li>The length (i.e. number of rows) of x equals the length of y</li>
 <li>x has at least one more row than it has columns (i.e. there is
 sufficient data to estimate regression coefficients for each of the
 columns in x plus an intercept.</li>
 </ul>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the [n,k] array representing the x data<DD><CODE>y</CODE> - the [n,1] array representing the y data
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>x</code> or <code>y</code> is null
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>x</code> and <code>y</code> do not
 have the same length
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</A></CODE> - if <code>x</code> or <code>y</code> are zero-length
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</A></CODE> - if the number of rows of <code>x</code>
 is not larger than the number of columns + 1</DL>
</DD>
</DL>
<HR>

<A NAME="validateCovarianceData(double[][], double[][])"><!-- --></A><H3>
validateCovarianceData</H3>
<PRE>
protected void <B>validateCovarianceData</B>(double[][]&nbsp;x,
                                      double[][]&nbsp;covariance)</PRE>
<DL>
<DD>Validates that the x data and covariance matrix have the same
 number of rows and that the covariance matrix is square.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the [n,k] array representing the x sample<DD><CODE>covariance</CODE> - the [n,n] array representing the covariance matrix
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the number of rows in x is not equal
 to the number of rows in covariance
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></CODE> - if the covariance matrix is not square</DL>
</DD>
</DL>
<HR>

<A NAME="estimateRegressionParameters()"><!-- --></A><H3>
estimateRegressionParameters</H3>
<PRE>
public double[] <B>estimateRegressionParameters</B>()</PRE>
<DL>
<DD>Estimates the regression parameters b.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateRegressionParameters()">estimateRegressionParameters</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>The [k,1] array representing b</DL>
</DD>
</DL>
<HR>

<A NAME="estimateResiduals()"><!-- --></A><H3>
estimateResiduals</H3>
<PRE>
public double[] <B>estimateResiduals</B>()</PRE>
<DL>
<DD>Estimates the residuals, ie u = y - X*b.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateResiduals()">estimateResiduals</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>The [n,1] array representing the residuals</DL>
</DD>
</DL>
<HR>

<A NAME="estimateRegressionParametersVariance()"><!-- --></A><H3>
estimateRegressionParametersVariance</H3>
<PRE>
public double[][] <B>estimateRegressionParametersVariance</B>()</PRE>
<DL>
<DD>Estimates the variance of the regression parameters, ie Var(b).
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateRegressionParametersVariance()">estimateRegressionParametersVariance</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>The [k,k] array representing the variance of b</DL>
</DD>
</DL>
<HR>

<A NAME="estimateRegressionParametersStandardErrors()"><!-- --></A><H3>
estimateRegressionParametersStandardErrors</H3>
<PRE>
public double[] <B>estimateRegressionParametersStandardErrors</B>()</PRE>
<DL>
<DD>Returns the standard errors of the regression parameters.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateRegressionParametersStandardErrors()">estimateRegressionParametersStandardErrors</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>standard errors of estimated regression parameters</DL>
</DD>
</DL>
<HR>

<A NAME="estimateRegressandVariance()"><!-- --></A><H3>
estimateRegressandVariance</H3>
<PRE>
public double <B>estimateRegressandVariance</B>()</PRE>
<DL>
<DD>Returns the variance of the regressand, ie Var(y).
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html#estimateRegressandVariance()">estimateRegressandVariance</A></CODE> in interface <CODE><A HREF="../../../../../../org/apache/commons/math3/stat/regression/MultipleLinearRegression.html" title="interface in org.apache.commons.math3.stat.regression">MultipleLinearRegression</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>The double representing the variance of y</DL>
</DD>
</DL>
<HR>

<A NAME="estimateErrorVariance()"><!-- --></A><H3>
estimateErrorVariance</H3>
<PRE>
public double <B>estimateErrorVariance</B>()</PRE>
<DL>
<DD>Estimates the variance of the error.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>estimate of the error variance<DT><B>Since:</B></DT>
  <DD>2.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="estimateRegressionStandardError()"><!-- --></A><H3>
estimateRegressionStandardError</H3>
<PRE>
public double <B>estimateRegressionStandardError</B>()</PRE>
<DL>
<DD>Estimates the standard error of the regression.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>regression standard error<DT><B>Since:</B></DT>
  <DD>2.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="calculateBeta()"><!-- --></A><H3>
calculateBeta</H3>
<PRE>
protected abstract <A HREF="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>calculateBeta</B>()</PRE>
<DL>
<DD>Calculates the beta of multiple linear regression in matrix notation.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>beta</DL>
</DD>
</DL>
<HR>

<A NAME="calculateBetaVariance()"><!-- --></A><H3>
calculateBetaVariance</H3>
<PRE>
protected abstract <A HREF="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>calculateBetaVariance</B>()</PRE>
<DL>
<DD>Calculates the beta variance of multiple linear regression in matrix
 notation.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>beta variance</DL>
</DD>
</DL>
<HR>

<A NAME="calculateYVariance()"><!-- --></A><H3>
calculateYVariance</H3>
<PRE>
protected double <B>calculateYVariance</B>()</PRE>
<DL>
<DD>Calculates the variance of the y values.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>Y variance</DL>
</DD>
</DL>
<HR>

<A NAME="calculateErrorVariance()"><!-- --></A><H3>
calculateErrorVariance</H3>
<PRE>
protected double <B>calculateErrorVariance</B>()</PRE>
<DL>
<DD><p>Calculates the variance of the error term.</p>
 Uses the formula <pre>
 var(u) = u &middot; u / (n - k)
 </pre>
 where n and k are the row and column dimensions of the design
 matrix X.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>error variance estimate<DT><B>Since:</B></DT>
  <DD>2.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="calculateResiduals()"><!-- --></A><H3>
calculateResiduals</H3>
<PRE>
protected <A HREF="../../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>calculateResiduals</B>()</PRE>
<DL>
<DD>Calculates the residuals of multiple linear regression in matrix
 notation.

 <pre>
 u = y - X * b
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>The residuals [n,1] matrix</DL>
</DD>
</DL>
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